Do I need to have nVidia Graphics card?

I'm asking due to Unity using PhysX for physics and read that it is used on nVidia Graphics cards only unless it's changed and if so does anyone know if PhysX can be used on ATi Radeon HD 5870?

PhysX in Unity is software-only. It doesn't know or care what graphics card you have. You don't actually think Unity would leave out the majority of systems, do you? (Which would unfortunately be those which have craptastic Intel integrated chips.)

No, you do not need an nVidia card.